Answer

b=4

Work Step by Step

The Pythagorean Theorem states that for a right triangle, $a^{2} +b^{2} = c^{2}$. Thus, we plug in the values given for a, b, or c, and then we use these values to find the missing value:
$.9^{2} + b^{2} = 4.1^{2} \\\\ .81+ b^{2} =16.81 \\\\ b^{2} =16 \\\\ b=4$